1. Field of the Invention
The invention relates to a method and system for rapidly decelerating a treadmill belt and more specifically relates to a method and system for rapidly decelerating a treadmill belt on a treadmill having a D.C. motor that changes the internal configurations of a transmission on a treadmill powered by a constant speed drive motor, which transmission connects the constant speed drive motor to the belt of the treadmill.
2. Description of Related Art
Treadmills require a drive motor to provide power to the treadmill's belt. Most often, these drive motors are AC motors which turn at only one speed which speed depends on the frequency of the AC power supply. In order to provide various speeds for the treadmill belt, these AC drive motors are connected to the treadmill belt through a mechanical transmission which changes its internal configuration to provide the various speeds for the treadmill belt. The internal configurations of the mechanical transmission is typically set by a relatively small speed-change motor. As the speed-change motor turns, the transmission's internal configuration changes so that the treadmill belt speed either increases or decreases depending on the direction that the speed-change motor is turning.
Referring to FIG. 1, a typical treadmill transmission, generally labelled 1, is shown. Typically, these transmissions have a pair of adjustable pulleys 4,7 connected by a transmission belt 6. A first pulley 4 is connected to a drive motor 2 through an input shaft 3 so that rotation of the drive motor 2 rotates this first pulley 4. This first pulley 4 has two opposing conical plates 5a,b which form a V-shape for frictionally receiving a correspondingly shaped transmission belt 6.
The transmission 1 also has a second pulley 7. The second pulley 7 has a set of opposed conical plates attached to an output shaft 9. The conical plates 8a,b of the second pulley 7 also form a V-shaped recess for frictionally receiving the transmission belt 6 therebetween. The output shaft 9 is in turn attached to a drive roller 11 through a drive belt 10. Rotation of the drive roller 11 causes the treadmill belt (not shown) to move.
Typically in such a transmission 1, a speed-change motor 12 moves the two plates 5a,b of the first pulley 4 either closer together or further apart. Because of the conical shape of the opposed plates 5a,b, as the plates are moved further apart and tension is placed on the transmission belt 6, the transmission belt 6 situated around the first pulley 4 will move closer to the center of the input shaft 3. As the two plates 5a,b are moved closer together by the speed-change motor 12, the transmission belt 6 is moved more towards the outer edge of the first pulley 4.
The plates 8a,b of the second pulley 7 are biased in a position toward each other by a tension spring 13. However, sufficient pressure by the transmission belt 6 on the conical plates 8a,b of the second pulley 7 will overcome the inherent bias of the plates to be together and force them apart thereby allowing the transmission belt 6, which is under tension, to move from a position more towards the outer edge of the plates 8a,b to a position closer towards the output shaft 9. In this way the mechanical advantage imparted to the drive roller 11, and subsequently to the treadmill belt from the drive motor 2, changes depending on the position of the transmission belt 6 on the first and second pulleys 4,7.
The rate of change of the speed of the treadmill belt is dependent on both the current speed of the treadmill belt, that is, on the current position of the transmission belt 6 on pulleys 4,7, and on how fast the speed-change motor 12 is turning.
Previous transmissions have used AC speed-change motors. However, under normal operating conditions, AC motors turn at only one speed regardless of the current or voltage applied to the motor. Consequently, the speed at which the opposing conical plates 5a,b are moved together or apart as driven by the AC speed change motor is a constant. In a transmission using an AC speed-change motor, the entire change in the speed of the treadmill belt results from the change in position of the transmission belt 6 on pulleys 4,7 and not from any change in the rate that the conical plates 5a,b are moved together or apart. A constant rate of moving the conical plates 5a,b together or apart as a result of the constant speed of the AC speed change motor 12 results in a non-constant rate of change for the speed of the treadmill belt as illustrated in FIG. 2.
This non-constant rate of speed change has two primary sources. First, the belt connecting the pulleys has a constant length. As shown in FIG. 1, as the plates 5a,b of the first pulley 4 move together or apart in response to the rotation of the speed-change motor 12, the location of the transmission belt 6 on plates 5a,b changes. As the conical plates 5a,b move apart, the transmission belt 6 will have less tension on it. As a result of the reduction of tension on the transmission belt 6, the tension spring 13 will push plates 8a,b together thereby moving transmission belt 6 farther away from the output shaft 9. As transmission belt 6 moves away from output shaft 9, tension is placed on transmission belt 6 by tension spring 13 pulling it into snug frictional contact with conical plates 5a,b at a position closer to input shaft 3 than it had been prior to conical plates 5 a,b moving apart in response to the rotation of speed change motor 12. Transmission belt 6 will move out from output shaft 9 until the tension in transmission belt 6 equals the tension applied by tension spring 13. This causes the mechanical ratio of pulley 4 and pulley 7 to change. This relationship is illustrated in FIG. 3.
The exact equation for the transmission belt circumference is found by the sum of the straight portions (l+l) and the two partial circumferences (c.sub.1 +c.sub.2). This leads to the following equation: EQU Circumference=2d.multidot.sin .theta.+2.theta..multidot.r.sub.1 +2(.pi.-.theta..multidot.r.sub.2) 1)
where:
.theta.=cos.sup.-1 ((r.sub.2 -r.sub.1)/d), and .theta. is in radians; PA1 r.sub.1 =the radius of the transmission belt 6 around first pulley 4; PA1 r.sub.2 =the radius of the transmission-belt 6 around second pulley 7; PA1 d=the distance between first pulley 4 and second pulley 7; and, PA1 1=d.multidot.sin .theta.=((d.sup.2 -(r.sub.2 -r.sub.1).sup.2).sup.1/2. PA1 d=8" PA1 C=31.6" PA1 K=3.19
This equation is extremely difficult to solve for r.sub.2 in terms of r.sub.1. Equation 1 can be simplified by making the following approximations: EQU c.sub.1 =.pi.r.sub.1 EQU c.sub.2 =.pi.r.sub.2, and EQU l=((d.sup.2 -(r.sub.2 -r.sub.1).sup.2).sup.1/2 +.pi.(r.sub.2 +r.sub.1)
so that: EQU Circumference=2((d.sup.2 -(r.sub.2 -r.sub.1).sup.2).sup.1/2 +.pi.(r.sub.2 -r.sub.1) 2)
The error created in this approximation is very small and creates an equation which is more easily solved. Since Circumference is the circumference of transmission belt 6 which is a constant "C", and "d", the distance between pulleys 4 and 7, is a constant, the following quadratic equation is derived: EQU (.pi.-4)r.sub.2.sup.2 +((2.pi..sup.2 +8)r.sub.1 -2.pi.C)r.sub.2 +((.pi..sup.2 -4)r.sub.1.sup.2 -2.pi.Cr.sub.1 +C.sup.2 -4d.sup.2)=0.3)
Solving for r.sub.2 gives: EQU r.sub.2 =(.pi.C-(.pi..sup.2 +4)r.sub.1 .+-.2(4.pi..sup.2 r.sub.1.sup.2 -4.pi.Cr.sub.1 +C.sup.2 +d.sup.2 (.pi..sup.2 -4)).sup.1/2)/(.pi..sup.2 -4)4)
Realistic values show the ".+-." factor is subtracted, only, in this application.
Although this equation is somewhat cumbersome, it describes the relationship between the position of transmission belt 6 on pulleys 4,7 very well. The treadmill belt speed is a function of the position of transmission belt 6 on pulleys 4,7 and a constant which represents such factors as the gear reduction from the drive motor 2 to the input shaft 3 of first pulley 4. The AC drive motor 2 turns the first pulley 4 with transmission belt 6 positioned on pulley 4 at a radius r.sub.1 at a given RPM after a "constant" gear reduction. The RPM at r.sub.1 translates into an RPM at r.sub.2 as described by equation 4. Rotation of r.sub.2 drives the drive roller 11 and thus the treadmill belt at another gear ratio which provides another constant. Thus, the treadmill belt speed can be described as: EQU Speed=K(r.sub.1 /r.sub.2) 5)
where "K" is a constant which includes all the individual constants described above. The following constant values were used to generate the graph in FIG. 3. All values are relatively close to those actually used in treadmills. EQU 1.12".ltoreq.r.sub.1 .ltoreq.3.60"
As can be seen, the speed change on the output pulley 7 per radial change of position of the belt along the input pulley is non-linear; the speed change when r.sub.1 is large occurring at a faster rate than when r.sub.1 is smaller. Consequently, no easy means exists to compensate for the fact that the rate of change of speed of the treadmill belt depends on the current setting of the transmission. The effect of this is that the treadmill belt changes speeds much more slowly when the transmission is set at slow speeds than it does when the transmission is set at high speeds. For example, using the transmission settings described above which produced the graph of FIG. 2, it takes about 12 seconds to change speed by one mile per hour from one mile per hour to two miles per hour. But, on the same transmission, it takes about 11/4 seconds to make a one mile per hour change from nine miles per hour to ten miles an hour.
Therefore, it is highly desirable to provide a system for changing the speed of the treadmill which changes speed at approximately the same rate regardless of the current setting of the transmission.
Another common problem with treadmills is that if they are shut off with their transmission set at high speed, when they are restarted, they will restart at this same high speed. An unsuspecting user of the treadmill, unaware that the treadmill has been shut off at a high speed, may attempt to restart the treadmill while standing on the belt. When the treadmill starts in this condition, it starts at a high speed. This has been known to cause unsuspecting users to fall as the treadmill belt moves their feet out from under their bodies. This has resulted in injury to the users as a result of the fall. Therefore it is highly desirable to provide a treadmill which is always starts at slow speed regardless of the speed of the treadmill when it is shut off.
In the typical treadmill, the normal deceleration rate from full speed to stop may be as long as 40 seconds. This has been found to be too long a time for the user to wait for the belt to stop. Consequently, typical treadmills are stopped at whatever speed their transmission configuration is set at and then allowed to restart at that same speed. In order to protect users from these high speed starts, a warning label is placed on the treadmill stating that the treadmill should not be started while standing on the belt because of the danger that the treadmill could start at a high speed. This type of warning has proved to be ineffective and consequently unacceptable because users either ignore the label or the label is either damaged or removed from the device.